Positively curved cohomogeneity one manifolds and 3-sasakian geometry

Karsten Grove University of Maryland Burkhard Wilking University of M¨unster Wolfgang Ziller University of Pennsylvania

Differential Geometry mathscidoc:1609.10048

Journal of Differential Geometry, 78, (1), 33-111, 2008
We provide an exhaustive description of all simply connected positively curved cohomogeneity one manifolds. The description yields a complete classification in all dimensions but 7, where in addition to known examples, our list contains one exceptional space and two infinite families not yet known to carry metrics of positive curvature. The infinite families also carry a 3-Sasakian metric of cohomogeneity one, which is associated to a family of selfdual Einstein orbifold metrics on the 4-sphere constructed by Hitchin.
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@inproceedings{karsten2008positively,
  title={POSITIVELY CURVED COHOMOGENEITY ONE MANIFOLDS AND 3-SASAKIAN GEOMETRY},
  author={Karsten Grove, Burkhard Wilking, and Wolfgang Ziller},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909103931009980705},
  booktitle={Journal of Differential Geometry},
  volume={78},
  number={1},
  pages={33-111},
  year={2008},
}
Karsten Grove, Burkhard Wilking, and Wolfgang Ziller. POSITIVELY CURVED COHOMOGENEITY ONE MANIFOLDS AND 3-SASAKIAN GEOMETRY. 2008. Vol. 78. In Journal of Differential Geometry. pp.33-111. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909103931009980705.
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